David Cameron and the German chancellor, Angela Merkel, have agreed to work together to make the European Union more competitive and flexible, Downing Street has said.

After talks at Merkel's guest residence, Schloss Meseberg, No 10 said the two leaders also agreed that the EU should be prepared to make an "ambitious offer" in trade talks with the US.

The prime minister used his overnight stay in the Brandenburg countryside to set out his plans to renegotiate Britain's relationship with Europe, but the Downing Street statement offered no clue as to how they were received.

Merkel is anxious that Britain should remain in the EU and has made no secret of her concerns about Cameron's plan to stage a referendum on membership if the Conservatives win the next general election in 2015.

"On the EU, the PM set out his approach to European reform, following on from his speech in January," the Downing Street statement said on Saturday. "They agreed on the urgent need to make Europe more competitive and flexible and talked about ways to achieve this. And they discussed how we can work together in the run-up to the May and June European councils to make further progress."

The leaders also discussed the forthcoming G8 summit, which Cameron is hosting at Lough Erne in Northern Ireland, and the need to show "global leadership" in tackling tax evasion and aggressive tax avoidance.

On Syria, where Merkel is resisting pressure from Britain and France to lift an EU arms embargo to allow equipment to go to the rebels, they agreed to keep working to find ways to increase pressure on Bashar al-Assad's regime while strengthening the moderate opposition.

In an unusual move seen as evidence of their good working relationship despite their differences on key issues, Merkel invited Cameron to bring his wife, Samantha, and their three children to stay at Schloss Meseberg, an elegant baroque manor set in picturesque grounds.